Uploaded October 2024 | Updated September 2026, 5 hours ago
#statistics #philosophy #datascience #probability #chance #bayesian
In this video, I'll explain what probability and chance are often meant to capture. I'll talk about the differences between the Frequentist and Bayesian perspectives.
NOTE: There are two typos at 14:52. The average or expected side length for cubes with a face area from 0 to 1 should be 2/3, and the average or expected side length of a cube with volume from 0 to 1 should be 3/4. This doesn't change the argument but these are the correct values for those integrals.
References:
[1] E. T. Bell, The Development of Mathematics. Courier Corporation, 2012.
[2] B. De Finetti, A. Machì, A. F. M. Smith, and B. De Finetti, Theory of probability: a critical introductory treatment. Chichester, UK ; Hoboken, NJ: John Wiley & Sons, 2017.
[3] R. W. Hamming, The Art of Probability for Scientists and Engineers. Redwood City, Calif: Addison-Wesley, 1991.
[4] A. N. Kolmogorov and A. T. Bharucha-Reid, Foundations of the Theory of Probability: Second English Edition. Courier Dover Publications, 2018.
[5] A. Hájek, “Interpretations of Probability,” in The Stanford Encyclopedia of Philosophy, Winter 2023., E. N. Zalta and U. Nodelman, Eds., Metaphysics Research Lab, Stanford University, 2023. Accessed: Jul. 18, 2024. [Online]. Available: https://plato.stanford.edu/archives/win2023/entries/probability-interpret/
[6] L. J. Savage, The Foundations of Statistics. Courier Corporation, 2012.
[7] A. D. Morgan, Formal Logic: Or, The Calculus of Inference, Necessary and Probable. Taylor and Walton, 1847.
[8] F. P. Ramsey, “Truth and Probability,” in Readings in Formal Epistemology: Sourcebook, H. Arló-Costa, V. F. Hendricks, and J. van Benthem, Eds., Cham: Springer International Publishing, 2016, pp. 21–45. doi:doi.org/10.1007/978-3-319-20451-2_3
[9] H. Reichenbach, The Theory of Probability: An Inquiry into the Logical and Mathematical Foundations of the Calculus of Probability (English Translsyion by Ernest H. Hutten and Maria Reichenbach)_ Repr. 2. ed. Berkeley: Univ. of California Pr, 1971.
[10] A. Hájek, “The reference class problem is your problem too,” Synthese, vol. 156, no. 3, pp. 563–585, Jun. 2007, doi: doi.org/10.1007/s11229-006-9138-5.
[11] J. M. Keynes, A Treatise on Probability. Courier Corporation, 2013.
[12] A. de Moivre, The Doctrine of Chances, Or, A Method of Calculating the Probabilites of Events in Play 1738.
[13] N. Shackel, “Bertrand’s Paradox and the Principle of Indifference,” Philosophy of Science, vol. 74, no. 2, pp. 150–175, Apr. 2007, doi: [10.1086/519028](https://doi.org/10.1086/519028).
[14] B. C. van Fraassen, Laws and Symmetry. Clarendon Press, 1989.
[15] E. T. Jaynes, “Information Theory and Statistical Mechanics. II,” _Phys. Rev._, vol. 108, no. 2, pp. 171–190, Oct. 1957, doi: [10.1103/PhysRev.108.171](https://doi.org/10.1103/PhysRev.108.171).
[16] C. S. Peirce, “Notes on the Doctrine of Chances,” in _Dispositions_, R. Tuomela, Ed., Dordrecht: Springer Netherlands, 1978, pp. 237–245. doi: [10.1007/978-94-017-1282-8_14](https://doi.org/10.1007/978-94-017-1282-8_14).
[17] E. Sober, Philosophy Of Biology, 2nd ed. New York: Routledge, 2019. doi: [10.4324/9780429494871](https://doi.org/10.4324/9780429494871).
[18] S. Oladyshkin and W. Nowak, “The Connection between Bayesian Inference and Information Theory for Model Selection, Information Gain and Experimental Design,” Entropy, vol. 21, no. 11, p. 1081, Nov. 2019, doi: [10.3390/e21111081](https://doi.org/10.3390/e21111081).
#statistics #philosophy #datascience #probability #chance #bayesian
In this video, I'll explain what probability and chance are often meant to capture. I'll talk about the differences between the Frequentist and Bayesian perspectives.
NOTE: There are two typos at 14:52. The average or expected side length for cubes with a face area from 0 to 1 should be 2/3, and the average or expected side length of a cube with volume from 0 to 1 should be 3/4. This doesn't change the argument but these are the correct values for those integrals.
References:
[1] E. T. Bell, The Development of Mathematics. Courier Corporation, 2012.
[2] B. De Finetti, A. Machì, A. F. M. Smith, and B. De Finetti, Theory of probability: a critical introductory treatment. Chichester, UK ; Hoboken, NJ: John Wiley & Sons, 2017.
[3] R. W. Hamming, The Art of Probability for Scientists and Engineers. Redwood City, Calif: Addison-Wesley, 1991.
[4] A. N. Kolmogorov and A. T. Bharucha-Reid, Foundations of the Theory of Probability: Second English Edition. Courier Dover Publications, 2018.
[5] A. Hájek, “Interpretations of Probability,” in The Stanford Encyclopedia of Philosophy, Winter 2023., E. N. Zalta and U. Nodelman, Eds., Metaphysics Research Lab, Stanford University, 2023. Accessed: Jul. 18, 2024. [Online]. Available: https://plato.stanford.edu/archives/win2023/entries/probability-interpret/
[6] L. J. Savage, The Foundations of Statistics. Courier Corporation, 2012.
[7] A. D. Morgan, Formal Logic: Or, The Calculus of Inference, Necessary and Probable. Taylor and Walton, 1847.
[8] F. P. Ramsey, “Truth and Probability,” in Readings in Formal Epistemology: Sourcebook, H. Arló-Costa, V. F. Hendricks, and J. van Benthem, Eds., Cham: Springer International Publishing, 2016, pp. 21–45. doi:doi.org/10.1007/978-3-319-20451-2_3
[9] H. Reichenbach, The Theory of Probability: An Inquiry into the Logical and Mathematical Foundations of the Calculus of Probability (English Translsyion by Ernest H. Hutten and Maria Reichenbach)_ Repr. 2. ed. Berkeley: Univ. of California Pr, 1971.
[10] A. Hájek, “The reference class problem is your problem too,” Synthese, vol. 156, no. 3, pp. 563–585, Jun. 2007, doi: doi.org/10.1007/s11229-006-9138-5.
[11] J. M. Keynes, A Treatise on Probability. Courier Corporation, 2013.
[12] A. de Moivre, The Doctrine of Chances, Or, A Method of Calculating the Probabilites of Events in Play 1738.
[13] N. Shackel, “Bertrand’s Paradox and the Principle of Indifference,” Philosophy of Science, vol. 74, no. 2, pp. 150–175, Apr. 2007, doi: [10.1086/519028](https://doi.org/10.1086/519028).
[14] B. C. van Fraassen, Laws and Symmetry. Clarendon Press, 1989.
[15] E. T. Jaynes, “Information Theory and Statistical Mechanics. II,” _Phys. Rev._, vol. 108, no. 2, pp. 171–190, Oct. 1957, doi: [10.1103/PhysRev.108.171](https://doi.org/10.1103/PhysRev.108.171).
[16] C. S. Peirce, “Notes on the Doctrine of Chances,” in _Dispositions_, R. Tuomela, Ed., Dordrecht: Springer Netherlands, 1978, pp. 237–245. doi: [10.1007/978-94-017-1282-8_14](https://doi.org/10.1007/978-94-017-1282-8_14).
[17] E. Sober, Philosophy Of Biology, 2nd ed. New York: Routledge, 2019. doi: [10.4324/9780429494871](https://doi.org/10.4324/9780429494871).
[18] S. Oladyshkin and W. Nowak, “The Connection between Bayesian Inference and Information Theory for Model Selection, Information Gain and Experimental Design,” Entropy, vol. 21, no. 11, p. 1081, Nov. 2019, doi: [10.3390/e21111081](https://doi.org/10.3390/e21111081).
